Mechanisms behind overshoots in mean cluster size profiles in aggregation-breakup processes

Abstract

Aggregation and breakup of small particles in stirred suspensions often shows an overshoot in the time evolution of the mean cluster size: Starting from a suspension of primary particles the mean cluster size first increases before going through a maximum beyond which a slow relaxation sets in. Such behavior was observed in various systems, including polymeric latices, inorganic colloids, asphaltenes, proteins, and, as shown by independent experiments in this work, in the flocculation of microalgae. This work aims at investigating possible mechanism to explain this phenomenon using detailed population balance modeling that incorporates refined rate models for aggregation and breakup of small particles in turbulence. Four mechanisms are considered: (1) restructuring, (2) decay of aggregate strength, (3) deposition of large clusters, and (4) primary particle aggregation where only aggregation events between clusters and primary particles are permitted. We show that all four mechanisms can lead to an overshoot in the mean size profile, while in contrast, aggregation and breakup alone lead to a monotonic, "S"-shaped size evolution profile. In order to distinguish between the different mechanisms simple protocols based on variations of the shear rate during the aggregation-breakup process are proposed.

Shear-Induced Heteroaggregation of Oppositely Charged Colloidal Particles

“…Once clusters attain a large-enough size, they become more vulnerable to breaking up as a consequence of the viscous stress exerted by the flow field. Therefore, in all of the suspensions in which a size-stabilization effect did not occur, a plateau value of ⟨ P ⟩ is expected to be reached at a later stage, as a consequence of an equilibrium between aggregation and breakage phenomena. − …”

Water Soluble Polymer Flocculants: Synthesis, Characterization, and Performance Assessment

“…Selomulya et al [18] proposed a population balance model based on restructuring, and that has been used by several researchers in modeling the polymer flocculation of particulate systems. [19][20][21][22][23] • Irreversible breakage: aggregates break apart, losing any chance of further re-aggregation, likely due to polymer chain rupture (carbon chain session) [24][25][26][27] or relaxation (reconformation) of the adsorbed polymer chains. [28][29][30] Both phenomena decrease the bridging capacity of the polymer chains, thus reducing aggregate size.…”

Aggregation modeling of the influence of pH on the aggregation of variably charged nanoparticles

“…The research on the aggregation of particles in the nano and micrometer size range is relevant in numerous processes, such as in the production of chemical materials and medicine, in environmental protection, and so forth [1][2][3] . The main factors affecting the aggregation of particles: pH [4][5][6] , solution temperature 6 , long-range van der Waals forces 7 , gravity 8 , electrolyte concentration, and electrolyte type 9 , particle size, the surface charge density of particles, etc.…”